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Question
Let * be the binary operation defined on Q. Find which of the following binary operations are commutative
a * b = a + ab ∀ a, b ∈ Q
Solution
Given that * is a binary operation defined on Q.
a * b = a + ab
b * a = b + ab
So clearly, a + ab ≠ b + ab
Thus, * is not commutative.
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